<!DOCTYPE html>
<html lang="zh-CN">

<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=2">
  <meta name="theme-color" content="#222">
  <meta name="generator" content="Hexo 4.2.1">
  <link rel="apple-touch-icon" sizes="180x180" href="/images/apple-touch-icon-next.png">
  <link rel="icon" type="image/png" sizes="32x32" href="/images/favicon-32x32-next.png">
  <link rel="icon" type="image/png" sizes="16x16" href="/images/favicon-16x16-next.png">
  <link rel="mask-icon" href="/images/safari-pinned-tab.svg" color="#222">
  <link rel="stylesheet" href="/css/main.css">
  <link rel="stylesheet" href="/lib/font-awesome/css/all.min.css">
  <link rel="stylesheet" href="/lib/pace/pace-theme-minimal.min.css">
  <script src="/lib/pace/pace.min.js"></script>
  <script id="hexo-configurations">
    var NexT = window.NexT ||
    {};
    var CONFIG = {
      "hostname": "cuiqingcai.com",
      "root": "/",
      "scheme": "Pisces",
      "version": "7.8.0",
      "exturl": false,
      "sidebar":
      {
        "position": "right",
        "width": 360,
        "display": "post",
        "padding": 18,
        "offset": 12,
        "onmobile": false,
        "widgets": [
          {
            "type": "image",
            "name": "阿布云",
            "enable": false,
            "url": "https://www.abuyun.com/http-proxy/introduce.html",
            "src": "https://qiniu.cuiqingcai.com/88au8.jpg",
            "width": "100%"
      },
          {
            "type": "image",
            "name": "天验",
            "enable": true,
            "url": "https://tutorial.lengyue.video/?coupon=12ef4b1a-a3db-11ea-bb37-0242ac130002_cqx_850",
            "src": "https://qiniu.cuiqingcai.com/bco2a.png",
            "width": "100%"
      },
          {
            "type": "image",
            "name": "华为云",
            "enable": false,
            "url": "https://activity.huaweicloud.com/2020_618_promotion/index.html?bpName=5f9f98a29e2c40b780c1793086f29fe2&bindType=1&salesID=wangyubei",
            "src": "https://qiniu.cuiqingcai.com/y42ik.jpg",
            "width": "100%"
      },
          {
            "type": "image",
            "name": "张小鸡",
            "enable": false,
            "url": "http://www.zxiaoji.com/",
            "src": "https://qiniu.cuiqingcai.com/fm72f.png",
            "width": "100%"
      },
          {
            "type": "image",
            "name": "Luminati",
            "src": "https://qiniu.cuiqingcai.com/ikkq9.jpg",
            "url": "https://luminati-china.io/?affiliate=ref_5fbbaaa9647883f5c6f77095",
            "width": "100%",
            "enable": false
      },
          {
            "type": "image",
            "name": "IPIDEA",
            "url": "http://www.ipidea.net/?utm-source=cqc&utm-keyword=?cqc",
            "src": "https://qiniu.cuiqingcai.com/0ywun.png",
            "width": "100%",
            "enable": true
      },
          {
            "type": "tags",
            "name": "标签云",
            "enable": true
      },
          {
            "type": "categories",
            "name": "分类",
            "enable": true
      },
          {
            "type": "friends",
            "name": "友情链接",
            "enable": true
      },
          {
            "type": "hot",
            "name": "猜你喜欢",
            "enable": true
      }]
      },
      "copycode":
      {
        "enable": true,
        "show_result": true,
        "style": "mac"
      },
      "back2top":
      {
        "enable": true,
        "sidebar": false,
        "scrollpercent": true
      },
      "bookmark":
      {
        "enable": false,
        "color": "#222",
        "save": "auto"
      },
      "fancybox": false,
      "mediumzoom": false,
      "lazyload": false,
      "pangu": true,
      "comments":
      {
        "style": "tabs",
        "active": "gitalk",
        "storage": true,
        "lazyload": false,
        "nav": null,
        "activeClass": "gitalk"
      },
      "algolia":
      {
        "hits":
        {
          "per_page": 10
        },
        "labels":
        {
          "input_placeholder": "Search for Posts",
          "hits_empty": "We didn't find any results for the search: ${query}",
          "hits_stats": "${hits} results found in ${time} ms"
        }
      },
      "localsearch":
      {
        "enable": true,
        "trigger": "auto",
        "top_n_per_article": 10,
        "unescape": false,
        "preload": false
      },
      "motion":
      {
        "enable": false,
        "async": false,
        "transition":
        {
          "post_block": "bounceDownIn",
          "post_header": "slideDownIn",
          "post_body": "slideDownIn",
          "coll_header": "slideLeftIn",
          "sidebar": "slideUpIn"
        }
      },
      "path": "search.xml"
    };

  </script>
  <meta name="description" content="位运算是我们在编程中常会遇到的操作，但仍然有很多开发者并不了解位运算，这就导致在遇到位运算时会“打退堂鼓”。实际上，位运算并没有那么复杂，只要我们了解其运算基础和运算符的运算规则，就能够掌握位运算的知识。接下来，我们一起学习位运算的相关知识。 程序中的数在计算机内存中都是以二进制的形式存在的，位运算就是直接对整数在内存中对应的二进制位进行操作。    注意：本文只讨论整数运算，小数运算不在本文研究">
  <meta property="og:type" content="article">
  <meta property="og:title" content="七分钟全面了解位运算">
  <meta property="og:url" content="https://cuiqingcai.com/6841.html">
  <meta property="og:site_name" content="静觅">
  <meta property="og:description" content="位运算是我们在编程中常会遇到的操作，但仍然有很多开发者并不了解位运算，这就导致在遇到位运算时会“打退堂鼓”。实际上，位运算并没有那么复杂，只要我们了解其运算基础和运算符的运算规则，就能够掌握位运算的知识。接下来，我们一起学习位运算的相关知识。 程序中的数在计算机内存中都是以二进制的形式存在的，位运算就是直接对整数在内存中对应的二进制位进行操作。    注意：本文只讨论整数运算，小数运算不在本文研究">
  <meta property="og:locale" content="zh_CN">
  <meta property="og:image" content="https://user-gold-cdn.xitu.io/2019/7/12/16be42ccba578426?w=448&amp;h=206&amp;f=png&amp;s=15358">
  <meta property="og:image" content="https://user-gold-cdn.xitu.io/2019/7/12/16be42d124cccad8?w=716&amp;h=858&amp;f=png&amp;s=110314">
  <meta property="og:image" content="https://user-gold-cdn.xitu.io/2019/7/12/16be42d36b70664e?w=720&amp;h=836&amp;f=png&amp;s=106105">
  <meta property="og:image" content="https://user-gold-cdn.xitu.io/2019/7/12/16be42de18183539?w=480&amp;h=152&amp;f=png&amp;s=14842">
  <meta property="og:image" content="https://user-gold-cdn.xitu.io/2019/7/12/16be42e0ef065859?w=745&amp;h=290&amp;f=png&amp;s=27444">
  <meta property="og:image" content="https://user-gold-cdn.xitu.io/2019/7/12/16be42e6eddfc892?w=530&amp;h=293&amp;f=png&amp;s=17694">
  <meta property="og:image" content="https://user-gold-cdn.xitu.io/2019/7/12/16be42f3a7eae3fa?w=608&amp;h=304&amp;f=jpeg&amp;s=73490">
  <meta property="article:published_time" content="2019-07-12T04:15:17.000Z">
  <meta property="article:modified_time" content="2021-12-18T13:11:11.561Z">
  <meta property="article:author" content="崔庆才">
  <meta property="article:tag" content="python">
  <meta property="article:tag" content="位运算">
  <meta name="twitter:card" content="summary">
  <meta name="twitter:image" content="https://user-gold-cdn.xitu.io/2019/7/12/16be42ccba578426?w=448&amp;h=206&amp;f=png&amp;s=15358">
  <link rel="canonical" href="https://cuiqingcai.com/6841.html">
  <script id="page-configurations">
    // https://hexo.io/docs/variables.html
    CONFIG.page = {
      sidebar: "",
      isHome: false,
      isPost: true,
      lang: 'zh-CN'
    };

  </script>
  <title>七分钟全面了解位运算 | 静觅</title>
  <meta name="google-site-verification" content="p_bIcnvirkFzG2dYKuNDivKD8-STet5W7D-01woA2fc" />
  <noscript>
    <style>
      .use-motion .brand,
      .use-motion .menu-item,
      .sidebar-inner,
      .use-motion .post-block,
      .use-motion .pagination,
      .use-motion .comments,
      .use-motion .post-header,
      .use-motion .post-body,
      .use-motion .collection-header
      {
        opacity: initial;
      }

      .use-motion .site-title,
      .use-motion .site-subtitle
      {
        opacity: initial;
        top: initial;
      }

      .use-motion .logo-line-before i
      {
        left: initial;
      }

      .use-motion .logo-line-after i
      {
        right: initial;
      }

    </style>
  </noscript>
  <link rel="alternate" href="/atom.xml" title="静觅" type="application/atom+xml">
</head>

<body itemscope itemtype="http://schema.org/WebPage">
  <div class="container">
    <div class="headband"></div>
    <header class="header" itemscope itemtype="http://schema.org/WPHeader">
      <div class="header-inner">
        <div class="site-brand-container">
          <div class="site-nav-toggle">
            <div class="toggle" aria-label="切换导航栏">
              <span class="toggle-line toggle-line-first"></span>
              <span class="toggle-line toggle-line-middle"></span>
              <span class="toggle-line toggle-line-last"></span>
            </div>
          </div>
          <div class="site-meta">
            <a href="/" class="brand" rel="start">
              <span class="logo-line-before"><i></i></span>
              <h1 class="site-title">静觅 <span class="site-subtitle"> 崔庆才的个人站点 </span>
              </h1>
              <span class="logo-line-after"><i></i></span>
            </a>
          </div>
          <div class="site-nav-right">
            <div class="toggle popup-trigger">
              <i class="fa fa-search fa-fw fa-lg"></i>
            </div>
          </div>
        </div>
        <nav class="site-nav">
          <ul id="menu" class="main-menu menu">
            <li class="menu-item menu-item-home">
              <a href="/" rel="section">首页</a>
            </li>
            <li class="menu-item menu-item-archives">
              <a href="/archives/" rel="section">文章列表</a>
            </li>
            <li class="menu-item menu-item-tags">
              <a href="/tags/" rel="section">文章标签</a>
            </li>
            <li class="menu-item menu-item-categories">
              <a href="/categories/" rel="section">文章分类</a>
            </li>
            <li class="menu-item menu-item-about">
              <a href="/about/" rel="section">关于博主</a>
            </li>
            <li class="menu-item menu-item-message">
              <a href="/message/" rel="section">给我留言</a>
            </li>
            <li class="menu-item menu-item-search">
              <a role="button" class="popup-trigger">搜索 </a>
            </li>
          </ul>
        </nav>
        <div class="search-pop-overlay">
          <div class="popup search-popup">
            <div class="search-header">
              <span class="search-icon">
                <i class="fa fa-search"></i>
              </span>
              <div class="search-input-container">
                <input autocomplete="off" autocapitalize="off" placeholder="搜索..." spellcheck="false" type="search" class="search-input">
              </div>
              <span class="popup-btn-close">
                <i class="fa fa-times-circle"></i>
              </span>
            </div>
            <div id="search-result">
              <div id="no-result">
                <i class="fa fa-spinner fa-pulse fa-5x fa-fw"></i>
              </div>
            </div>
          </div>
        </div>
      </div>
    </header>
    <div class="back-to-top">
      <i class="fa fa-arrow-up"></i>
      <span>0%</span>
    </div>
    <div class="reading-progress-bar"></div>
    <main class="main">
      <div class="main-inner">
        <div class="content-wrap">
          <div class="content post posts-expand">
            <article itemscope itemtype="http://schema.org/Article" class="post-block single" lang="zh-CN">
              <link itemprop="mainEntityOfPage" href="https://cuiqingcai.com/6841.html">
              <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
                <meta itemprop="image" content="/images/avatar.png">
                <meta itemprop="name" content="崔庆才">
                <meta itemprop="description" content="崔庆才的个人站点，记录生活的瞬间，分享学习的心得。">
              </span>
              <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
                <meta itemprop="name" content="静觅">
              </span>
              <header class="post-header">
                <h1 class="post-title" itemprop="name headline"> 七分钟全面了解位运算 </h1>
                <div class="post-meta">
                  <span class="post-meta-item">
                    <span class="post-meta-item-icon">
                      <i class="far fa-user"></i>
                    </span>
                    <span class="post-meta-item-text">作者</span>
                    <span><a href="/authors/韦世东学算法和反爬虫" class="author" itemprop="url" rel="index">韦世东学算法和反爬虫</a></span>
                  </span>
                  <span class="post-meta-item">
                    <span class="post-meta-item-icon">
                      <i class="far fa-calendar"></i>
                    </span>
                    <span class="post-meta-item-text">发表于</span>
                    <time title="创建时间：2019-07-12 12:15:17" itemprop="dateCreated datePublished" datetime="2019-07-12T12:15:17+08:00">2019-07-12</time>
                  </span>
                  <span class="post-meta-item">
                    <span class="post-meta-item-icon">
                      <i class="far fa-folder"></i>
                    </span>
                    <span class="post-meta-item-text">分类于</span>
                    <span itemprop="about" itemscope itemtype="http://schema.org/Thing">
                      <a href="/categories/%E6%8A%80%E6%9C%AF%E6%9D%82%E8%B0%88/" itemprop="url" rel="index"><span itemprop="name">技术杂谈</span></a>
                    </span>
                  </span>
                  <span id="/6841.html" class="post-meta-item leancloud_visitors" data-flag-title="七分钟全面了解位运算" title="阅读次数">
                    <span class="post-meta-item-icon">
                      <i class="fa fa-eye"></i>
                    </span>
                    <span class="post-meta-item-text">阅读次数：</span>
                    <span class="leancloud-visitors-count"></span>
                  </span>
                  <span class="post-meta-item" title="本文字数">
                    <span class="post-meta-item-icon">
                      <i class="far fa-file-word"></i>
                    </span>
                    <span class="post-meta-item-text">本文字数：</span>
                    <span>5.4k</span>
                  </span>
                  <span class="post-meta-item" title="阅读时长">
                    <span class="post-meta-item-icon">
                      <i class="far fa-clock"></i>
                    </span>
                    <span class="post-meta-item-text">阅读时长 &asymp;</span>
                    <span>5 分钟</span>
                  </span>
                </div>
              </header>
              <div class="post-body" itemprop="articleBody">
                <div class="advertisements">
                  <div class="item">
                    <a href="http://i0k.cn/4UUsd" target="_blank">
                      <img src="https://qiniu.cuiqingcai.com/dsdhf.jpg">
                    </a>
                  </div>
                </div>
                <p>位运算是我们在编程中常会遇到的操作，但仍然有很多开发者并不了解位运算，这就导致在遇到位运算时会“打退堂鼓”。实际上，位运算并没有那么复杂，只要我们了解其运算基础和运算符的运算规则，就能够掌握位运算的知识。接下来，我们一起学习位运算的相关知识。 程序中的数在计算机内存中都是以二进制的形式存在的，位运算就是直接对整数在内存中对应的二进制位进行操作。</p>
                <blockquote>
                  <p>注意：本文只讨论整数运算，小数运算不在本文研究之列</p>
                </blockquote>
                <h2 id="位运算的基础"><a href="#位运算的基础" class="headerlink" title="位运算的基础"></a>位运算的基础</h2>
                <p>我们常用的 <code>3</code>， <code>5</code> 等数字是十进制表示，而位运算的基础是二进制。即人类采用十进制，机器采用的是二进制，要深入了解位运算，就需要了解十进制和二进制的转换方法和对应关系。</p>
                <h3 id="二进制"><a href="#二进制" class="headerlink" title="二进制"></a>二进制</h3>
                <p>十进制转二进制时，采用“除 2 取余，逆序排列”法：</p>
                <ol>
                  <li>用 2 整除十进制数，得到商和余数;</li>
                  <li>再用 2 整除商，得到新的商和余数;</li>
                  <li>重复第 1 和第 2 步，直到商为 0;</li>
                  <li>将先得到的余数作为二进制数的高位，后得到的余数作为二进制数的低位，依次排序;</li>
                </ol>
                <p>排序结果就是该十进制数的二进制表示。例如十进制数 <code>101</code> 转换为二进制数的计算过程如下：</p>
                <figure class="highlight basic">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="symbol">101 </span>% <span class="number">2</span> = <span class="number">50</span> 余 <span class="number">1</span></span><br><span class="line"><span class="symbol">50 </span>% <span class="number">2</span> = <span class="number">25</span> 余 <span class="number">0</span></span><br><span class="line"><span class="symbol">25 </span>% <span class="number">2</span> = <span class="number">12</span> 余 <span class="number">1</span></span><br><span class="line"><span class="symbol">12 </span>% <span class="number">2</span> = <span class="number">6</span> 余 <span class="number">0</span></span><br><span class="line"><span class="symbol">6 </span>% <span class="number">2</span> = <span class="number">3</span> 余 <span class="number">0</span></span><br><span class="line"><span class="symbol">3 </span>% <span class="number">2</span> = <span class="number">1</span> 余 <span class="number">1</span></span><br><span class="line"><span class="symbol">1 </span>% <span class="number">2</span> = <span class="number">0</span> 余 <span class="number">1</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>逆序排列即二进制中的从高位到低位排序，得到 <code>7</code> 位二进制数为 <code>1100101</code>，如果要转换为 <code>8</code> 位二进制数，就需要在最高位补 <code>0</code>。即十进制数的 <code>8</code> 位二进制数为 <code>01100101</code>。 其完整过程如下图所示： <img src="https://user-gold-cdn.xitu.io/2019/7/12/16be42ccba578426?w=448&amp;h=206&amp;f=png&amp;s=15358" alt=""> 有网友整理了常见的进制与 ASCII 码对照表，表内容如下： ASCII 控制字符 <img src="https://user-gold-cdn.xitu.io/2019/7/12/16be42d124cccad8?w=716&amp;h=858&amp;f=png&amp;s=110314" alt=""> ASCII 可显示字符 <img src="https://user-gold-cdn.xitu.io/2019/7/12/16be42d36b70664e?w=720&amp;h=836&amp;f=png&amp;s=106105" alt=""></p>
                <h3 id="补码"><a href="#补码" class="headerlink" title="补码"></a>补码</h3>
                <p>现在，我们已经了解到二进制与十进制的换算方法，并拥有了进制对照表。但在开始学习位运算符之前，我们还需要了解补码的知识。 数值有正负之分，那么仅有 <code>0</code> 和 <code>1</code> 的二进制如何表示正负呢？ 人们设定，二进制中最高位为 <code>0</code> 代表正，为 <code>1</code> 则代表负。例如 <code>0000 1100</code> 对应的十进制为 <code>12</code>，而 <code>1000 1100</code> 对应的十进制为 <code>\-12</code>。这种表示被称作原码。但新的问题出现了，原本二进制的最高位始终为 <code>0</code>，为了表示正负又多出了 <code>1</code>，在执行运算时就会出错。举个例子，<code>1 + (-2)</code> 的二进制运算如下：</p>
                <figure class="highlight asciidoc">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line">0000 0001 + 1000 0010 </span><br><span class="line"><span class="section">= 1000 0011</span></span><br><span class="line"><span class="section">= -3</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>这显然是有问题的，问题就处在这个代表正负的最高位。接着，人们又弄出了反码（二进制各位置的 <code>0</code> 与 <code>1</code> 互换，例如 <code>0000 1100</code> 的反码为 <code>1111 0011</code>）。此时，运算就会变成这样：</p>
                <figure class="highlight asciidoc">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line">0000 0001 + 1111 1101</span><br><span class="line"><span class="section">= 1111 1110</span></span><br><span class="line"># 在转换成十进制前，需要再次反码</span><br><span class="line"><span class="section">= 1000 0001 </span></span><br><span class="line"><span class="section">= -1</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>这次好像正确了。但它仍然有例外，我们来看一下 <code>1 + (-1)</code>：</p>
                <figure class="highlight asciidoc">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line">0000 0001 <span class="code">+ 1111 +</span> 1110</span><br><span class="line"><span class="section">= 1111 1111</span></span><br><span class="line"><span class="section">= 1000 0000</span></span><br><span class="line"><span class="section">= -0</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>零是没有正负之分的，为了解决这个问题，就搞出了补码的概念。补码是为了让负数变成能够加的正数，所以 <code>负数的补码= 负数的绝对值取反 + 1</code>，例如 <code>\-1</code> 的补码为：</p>
                <figure class="highlight asciidoc">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line">\-1 的绝对值 1</span><br><span class="line"><span class="section">= 0000 0001 # 1 的二进制原码</span></span><br><span class="line"><span class="section">= 1111 1110 # 原码取反</span></span><br><span class="line"><span class="section">= 1111 1111 # +1 后得到补码</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p><code>\-1</code> 补码推导的完整过程如下图所示： <img src="https://user-gold-cdn.xitu.io/2019/7/12/16be42de18183539?w=480&amp;h=152&amp;f=png&amp;s=14842" alt=""> 反过来，由补码推导原码的过程为 <code>原码 = 补码 - 1，再求反</code>。要注意的是，反码过程中，最高位的值不变，这样才能够保证结果的正负不会出错。例如 <code>1 + (-6)</code> 和 <code>1 + (-9)</code> 的运算过程如下：</p>
                <figure class="highlight asciidoc">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"># 1 的补码 + -6 的补码</span><br><span class="line">0000 0001 + 1111 1010</span><br><span class="line"><span class="section">= 1111 1011 # 补码运算结果</span></span><br><span class="line"><span class="section">= 1111 1010 # 对补码减 1，得到反码</span></span><br><span class="line"><span class="section">= 1000 0101 # 反码取反，得到原码</span></span><br><span class="line"><span class="section">= -5 # 对应的十进制</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <figure class="highlight asciidoc">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"># 1 的补码 + -9 的补码</span><br><span class="line">0000 0001 + 1111 0111</span><br><span class="line"><span class="section">= 1111 1000 # 补码运算结果</span></span><br><span class="line"><span class="section">= 1111 0111 # 对补码减 1，得到反码</span></span><br><span class="line"><span class="section">= 1000 1000 # 反码取反，得到原码</span></span><br><span class="line"><span class="section">= -8 # 对应的十进制</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>要注意的是，正数的补码与原码相同，不需要额外运算。也可以说，补码的出现就是为了解决负数运算时的符号问题。</p>
                <blockquote>
                  <p>人生苦短 我用 Python。 崔庆才|静觅 邀请你关注微信公众号：进击的Coder</p>
                </blockquote>
                <h2 id="运算符介绍"><a href="#运算符介绍" class="headerlink" title="运算符介绍"></a>运算符介绍</h2>
                <p>位运算分为 6 种，它们是：</p>
                <p>名称</p>
                <p>符号</p>
                <p>按位与</p>
                <p>&amp;</p>
                <p>按位或</p>
                <p>|</p>
                <p>按位异或</p>
                <p>^</p>
                <p>按位取反</p>
                <p>~</p>
                <p>左移运算</p>
                <p>&lt;&lt;</p>
                <p>右移运算</p>
                <p>>&gt;</p>
                <h3 id="按位与"><a href="#按位与" class="headerlink" title="按位与"></a>按位与</h3>
                <p>按位与运算将参与运算的两数对应的二进制位相与，当对应的二进制位均为 <code>1</code> 时，结果位为 <code>1</code>，否则结果位为 <code>0</code>。按位与运算的运算符为 <code>&amp;</code>，参与运算的数以补码方式出现。举个例子，将数字 <code>5</code> 和数字 <code>8</code> 进行按位与运算，其实是将数字 <code>5</code> 对应的二进制 <code>0000 0101</code> 和数字 <code>8</code> 对应的二进制 <code>0000 1000</code> 进行按位与运算，即：</p>
                <figure class="highlight angelscript">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="number">0000</span> <span class="number">0101</span></span><br><span class="line">&amp;</span><br><span class="line"><span class="number">0000</span> <span class="number">1000</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>根据按位与的规则，将各个位置的数进行比对。运算过程如下：</p>
                <figure class="highlight angelscript">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="number">0000</span> <span class="number">0101</span></span><br><span class="line">&amp;</span><br><span class="line"><span class="number">0000</span> <span class="number">1000</span></span><br><span class="line">---- ----</span><br><span class="line"><span class="number">0000</span> <span class="number">0000</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>由于它们对应位置中没有“均为 <code>1</code> ”的情况，所以得到的结果是 <code>0000 0000</code>。数字 <code>5</code> 和 <code>8</code> 按位与运算的完整过程如下图： <img src="https://user-gold-cdn.xitu.io/2019/7/12/16be42e0ef065859?w=745&amp;h=290&amp;f=png&amp;s=27444" alt=""> 将结果换算成十进制，得到 <code>0</code>，即 <code>5&amp;8 = 0</code>。</p>
                <h3 id="按位或"><a href="#按位或" class="headerlink" title="按位或"></a>按位或</h3>
                <p>按位或运算将参与运算的两数对应的二进制位相或，只要对应的二进制位中有 <code>1</code>，结果位为 <code>1</code>，否则结果位为 <code>0</code>。按位或运算的运算符为 <code>|</code>，参与运算的数以补码方式出现。举个例子，将数字 <code>3</code> 和数字 <code>7</code> 进行按位或运算，其实是将数字 <code>3</code> 对应的二进制 <code>0000 0011</code>和数字 <code>7</code> 对应的二进制 <code>0000 0111</code> 进行按位或运算，即：</p>
                <figure class="highlight angelscript">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="number">0000</span> <span class="number">0011</span></span><br><span class="line">|</span><br><span class="line"><span class="number">0000</span> <span class="number">0111</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>根据按位或的规则，将各个位置的数进行比对。运算过程如下：</p>
                <figure class="highlight angelscript">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="number">0000</span> <span class="number">0011</span></span><br><span class="line">|</span><br><span class="line"><span class="number">0000</span> <span class="number">0111</span></span><br><span class="line">---- ----</span><br><span class="line"><span class="number">0000</span> <span class="number">0111</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>最终得到的结果为 <code>0000 0111</code>。将结果换算成十进制，得到 <code>7</code>，即 <code>3|7 = 7</code>。</p>
                <h3 id="按位异或"><a href="#按位异或" class="headerlink" title="按位异或"></a>按位异或</h3>
                <p>按位异或运算将参与运算的两数对应的二进制位相异或，当对应的二进制位值不同时，结果位为 <code>1</code>，否则结果位为 <code>0</code>。按位异或的运算符为 <code>^</code>，参与运算的数以补码方式出现。举个例子，将数字 <code>12</code> 和数字 <code>7</code> 进行按位异或运算，其实是将数字 <code>12</code> 对应的二进制 <code>0000 1100</code> 和数字 <code>7</code> 对应的二进制 <code>0000 0111</code> 进行按位异或运算，即：</p>
                <figure class="highlight angelscript">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="number">0000</span> <span class="number">1100</span></span><br><span class="line">^</span><br><span class="line"><span class="number">0000</span> <span class="number">0111</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>根据按位异或的规则，将各个位置的数进行比对。运算过程如下：</p>
                <figure class="highlight angelscript">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="number">0000</span> <span class="number">1100</span></span><br><span class="line">^</span><br><span class="line"><span class="number">0000</span> <span class="number">0111</span></span><br><span class="line">---- ----</span><br><span class="line"><span class="number">0000</span> <span class="number">1011</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>最终得到的结果为 <code>0000 1011</code>。将结果换算成十进制，得到 <code>11</code>，即 <code>12^7 = 11</code>。</p>
                <h3 id="按位取反"><a href="#按位取反" class="headerlink" title="按位取反"></a>按位取反</h3>
                <p>按位取反运算将二进制数的每一个位上面的 <code>0</code> 换成 <code>1</code>，<code>1</code> 换成 <code>0</code>。按位取反的运算符为 <code>~</code>，参与运算的数以补码方式出现。举个例子，对数字 <code>9</code> 进行按位取反运算，其实是将数字 <code>9</code> 对应的二进制 <code>0000 1001</code> 进行按位取反运算，即：</p>
                <figure class="highlight asciidoc">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line">～0000 1001</span><br><span class="line"><span class="section">= 0000 1001 # 补码，正数补码即原码</span></span><br><span class="line"><span class="section">= 1111 1010 # 取反</span></span><br><span class="line"><span class="section">= -10</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>最终得到的结果为 <code>\-10</code>。再来看一个例子，<code>\-20</code> 按位取反的过程如下：</p>
                <figure class="highlight asciidoc">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line">～0001 0100</span><br><span class="line"><span class="section">= 1110 1100 # 补码</span></span><br><span class="line"><span class="section">= 0001 0011 # 取反</span></span><br><span class="line"><span class="section">= 19</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>最终得到的结果为 <code>19</code>。我们从示例中找到了规律，按位取反的结果用数学公式表示： <script type="math/tex">～x = -(x + 1)</script> 我们可以将其套用在 <code>9</code> 和 <code>\-20</code> 上：</p>
                <figure class="highlight angelscript">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line">～<span class="number">9</span> = -(<span class="number">9</span> + <span class="number">1</span>) = <span class="number">-10</span></span><br><span class="line">~(<span class="number">-20</span>) = -((<span class="number">-20</span>) + <span class="number">1</span>) = <span class="number">19</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>这个规律也可以作用于数字 <code>0</code> 上，即 <code>~0 = -(0 + 1) = -1</code>。</p>
                <h3 id="左移运算"><a href="#左移运算" class="headerlink" title="左移运算"></a>左移运算</h3>
                <p>左移运算将数对应的二进位全部向左移动若干位，高位丢弃，低位补 <code>0</code>。左移运算的运算符为 <code>&lt;&lt;</code>。举个例子，将数字 <code>5</code> 左移 <code>4</code> 位，其实是将数字 <code>5</code> 对应的二进制 <code>0000 0101</code> 中的二进位向左移动 <code>4</code> 位，即：</p>
                <figure class="highlight asciidoc">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line">5 &lt;&lt; 4</span><br><span class="line"><span class="section">= 0000 0101 &lt;&lt; 4</span></span><br><span class="line"><span class="section">= 0101 0000 # 高位丢弃，低位补 0</span></span><br><span class="line"><span class="section">= 80</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>数字 <code>5</code> 左移 <code>4</code> 位的完整运算过程如下图： <img src="https://user-gold-cdn.xitu.io/2019/7/12/16be42e6eddfc892?w=530&amp;h=293&amp;f=png&amp;s=17694" alt=""> 最终结果为 <code>80</code>。这等效于: <script type="math/tex">5 _ (2) ^4</script> 也就是说，左移运算的规律为： <script type="math/tex">x << n = x _ (2) ^ n</script>
                </p>
                <h3 id="右移运算"><a href="#右移运算" class="headerlink" title="右移运算"></a>右移运算</h3>
                <p>右移运算将数对应的二进位全部向右移动若干位。对于左边的空位，如果是正数则补 <code>0</code>，负数可能补 <code>0</code> 或 <code>1</code> （Turbo C 和很多编译器选择补 <code>1</code>）。右移运算的运算符为 <code>\&gt;&gt;</code>。举个例子，将数字 <code>80</code> 右移 <code>4</code> 位，其实是将数字 <code>80</code> 对应的二进制 <code>0101 0000</code> 中的二进位向右移动 <code>4</code> 位，即：</p>
                <figure class="highlight asciidoc">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line">80 &gt;&gt; 4</span><br><span class="line"><span class="section">= 0101 0000 &gt;&gt; 4</span></span><br><span class="line"><span class="section">= 0000 0101 # 正数补0，负数补1 </span></span><br><span class="line"><span class="section">= 5</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>最终结果为 <code>5</code>。这等效于： <script type="math/tex">80 \\div (2)^4</script> 也就是说，右移运算的规律为： <script type="math/tex">x >> n = x \\div (2) ^ n</script> 要注意的是，不能整除时，取整数。这中除法取整的规则类似于 <code>PYTHON</code> 语言中的地板除。</p>
                <blockquote>
                  <p>超酷人生 我用 Rust 韦世东|奎因 邀请你关注微信公众号：Rust之禅</p>
                </blockquote>
                <h2 id="位运算的应用"><a href="#位运算的应用" class="headerlink" title="位运算的应用"></a>位运算的应用</h2>
                <p>在掌握了位运算的知识后，我们可以在开发中尝试使用它。坊间一直流传着位运算的效率高，速度快，但从未见过文献证明，所以本文不讨论效率和速度的问题。如果正在阅读文章的你有相关文献，请留言告知，谢谢。 <strong>判断数字奇偶</strong> 通常，我们会通过取余来判断数字是奇数还是偶数。例如判断 <code>101</code> 的奇偶用的方法是：</p>
                <figure class="highlight routeros">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="comment"># python</span></span><br><span class="line"><span class="keyword">if</span> 101 % 2:</span><br><span class="line">    <span class="builtin-name">print</span>(<span class="string">'偶数'</span>)</span><br><span class="line"><span class="keyword">else</span>:</span><br><span class="line">    <span class="builtin-name">print</span>(<span class="string">'奇数'</span>)</span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>我们也可以通过位运算中的按位与来实现奇偶判断，例如：</p>
                <figure class="highlight routeros">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="comment"># python</span></span><br><span class="line"><span class="keyword">if</span> 101 &amp; 1:</span><br><span class="line">    <span class="builtin-name">print</span>(<span class="string">'奇数'</span>)</span><br><span class="line"><span class="keyword">else</span>:</span><br><span class="line">    <span class="builtin-name">print</span>(<span class="string">'偶数'</span>)</span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>这是因为奇数的二进制最低位始终为 <code>1</code>，而偶数的二进制最低为始终为 <code>0</code>。所以，无论任何奇数与 <code>1</code> 即 <code>0000 0001</code> 相与得到的都是 <code>1</code>，任何偶数与其相与得到的都是 <code>0</code>。 <strong>变量交换</strong> 在 C 语言中，两个变量的交换必须通过第三个变量来实现。伪代码如下：</p>
                <figure class="highlight asciidoc">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"># 伪代码</span><br><span class="line">a = 3, b = 5</span><br><span class="line">c = a</span><br><span class="line">a = b</span><br><span class="line">b = a</span><br><span class="line">--------</span><br><span class="line">a = 5, b = 3</span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>在 PYTHON 语言中并没有这么麻烦，可以直接交换。对应的 PYTHON 代码如下：</p>
                <figure class="highlight livecodeserver">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="comment"># python</span></span><br><span class="line"><span class="keyword">a</span>, b = <span class="number">3</span>, <span class="number">5</span></span><br><span class="line"><span class="keyword">a</span>, b = b, <span class="keyword">a</span></span><br><span class="line">print(<span class="keyword">a</span>, b)</span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>代码运行结果为 <code>5 3</code>。但大部分编程语言都不支持 PYTHON 这种写法，在这种情况下我们可以通过位运算中的按位异或来实现变量的交换。对应的伪代码如下：</p>
                <figure class="highlight ini">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="comment"># 伪代码</span></span><br><span class="line"><span class="attr">a</span> = <span class="number">3</span>, b = <span class="number">5</span></span><br><span class="line"><span class="attr">a</span> = a ^ b</span><br><span class="line"><span class="attr">b</span> = a ^ b</span><br><span class="line"><span class="attr">a</span> = a ^ b</span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>最后，<code>a = 5, b = 3</code>。我们可以用 C 语言和 PYTHON 语言进行验证，对应的 PYTHON 代码如下：</p>
                <figure class="highlight livecodeserver">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="comment"># python</span></span><br><span class="line"><span class="keyword">a</span>, b = <span class="number">3</span>, <span class="number">5</span></span><br><span class="line"><span class="keyword">a</span> = <span class="keyword">a</span> ^ b</span><br><span class="line">b = <span class="keyword">a</span> ^ b</span><br><span class="line"><span class="keyword">a</span> = <span class="keyword">a</span> ^ b</span><br><span class="line">print(<span class="keyword">a</span>, b)</span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>代码运行结果为 <code>5 3</code>，说明变量交换成功。对应的 C 代码如下：</p>
                <figure class="highlight cpp">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;stdio.h&gt;</span></span></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">int</span> a = <span class="number">3</span>, b = <span class="number">5</span>;</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">"交换前：a=%d , b=%dn"</span>,a,b);</span><br><span class="line">    a = a^b;</span><br><span class="line">    b = a^b;</span><br><span class="line">    a = a^b;</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">"交换后：a=%d , b=%dn"</span>,a, b);           </span><br><span class="line">&#125;</span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>代码运行结果如下：</p>
                <figure class="highlight routeros">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line">交换前：<span class="attribute">a</span>=3 , <span class="attribute">b</span>=5</span><br><span class="line">交换后：<span class="attribute">a</span>=5 , <span class="attribute">b</span>=3</span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>这说明变量交换成功。 <strong>求 x 与 2 的 n 次方乘积</strong> 设一个数为 <code>x</code>，求 <code>x</code> 与 <code>2</code> 的 <code>n</code> 次方乘积。这用数学来计算都是非常简单的： <script type="math/tex">x * (2) ^ n</script> 在位运算中，要实现这个需求只需要用到左移运算，即 <code>x &lt;&lt; n</code>。 <strong>取 x 的第 k 位</strong> 即取数字 <code>x</code> 对应的二进制的第 <code>k</code> 位上的二进制值。假设数字为 <code>5</code>，其对应的二进制为 <code>0000 0101</code>，取第 <code>k</code> 位二进制值的位运算为 <code>x &gt;&gt; k &amp; 1</code>。我们可以用 PYTHON 代码进行验证：</p>
                <figure class="highlight angelscript">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"># python</span><br><span class="line">x = <span class="number">5</span>  # <span class="number">0000</span> <span class="number">0101</span></span><br><span class="line"><span class="keyword">for</span> i <span class="keyword">in</span> range(<span class="number">8</span>):</span><br><span class="line">    print(x &gt;&gt; i &amp; <span class="number">1</span>)</span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>代码运行结果如下：</p>
                <figure class="highlight angelscript">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="number">1</span></span><br><span class="line"><span class="number">0</span></span><br><span class="line"><span class="number">1</span></span><br><span class="line"><span class="number">0</span></span><br><span class="line"><span class="number">0</span></span><br><span class="line"><span class="number">0</span></span><br><span class="line"><span class="number">0</span></span><br><span class="line"><span class="number">0</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>这说明位运算的算法是正确的，可以满足我们的需求。 <strong>判断赋值</strong></p>
                <figure class="highlight gml">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="keyword">if</span> a == <span class="symbol">x</span>:</span><br><span class="line">    <span class="symbol">x</span> = b</span><br><span class="line"><span class="keyword">else</span>:</span><br><span class="line">    <span class="symbol">x</span> = a</span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>等效于 <code>x = a ^ b ^ x</code>。我们可以通过 PYTHON 代码来验证：</p>
                <figure class="highlight sas">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"># python</span><br><span class="line">a, b, <span class="meta">x</span> = 6, 9, 6</span><br><span class="line"><span class="meta">if</span> a == <span class="meta">x</span>:</span><br><span class="line">    <span class="meta">x</span> = b</span><br><span class="line"><span class="meta">else</span>:</span><br><span class="line">    <span class="meta">x</span> = a</span><br><span class="line">p<span class="meta">rint(</span>a, b, <span class="meta">x</span>)</span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>代码运行结果为 <code>699</code>，与之等效的代码如下：</p>
                <figure class="highlight sas">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"># python</span><br><span class="line">a, b, <span class="meta">x</span> = 6, 9, 6</span><br><span class="line"><span class="meta">x</span> = a ^ b ^ <span class="meta">x</span></span><br><span class="line">p<span class="meta">rint(</span>a, b, <span class="meta">x</span>)</span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>这样就省去了 <code>if else</code> 的判断语句。 <strong>代替地板除</strong> 二分查找是最常用的算法之一，但它有一定的前提条件：二分查找的目标必须采用顺序存储结构，且元素有序排列。例如 PYTHON 中的有序列表。二分查找的最优复杂度为 <code>O(1)</code>，最差时间复杂度为 <code>O(log n)</code>。举个例子，假设我们需要从列表 <code>[1, 3, 5, 6, 7, 8, 12, 22, 23, 43, 65, 76, 90, 543]</code> 中找到指定元素的下标，对应的 PYTHON 代码如下：</p>
                <figure class="highlight yaml">
                  <table>
                    <tr>
                      <td class="gutter">
                        <pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br></pre>
                      </td>
                      <td class="code">
                        <pre><span class="line"><span class="comment"># python</span></span><br><span class="line"><span class="string">def</span> <span class="string">search(lis:</span> <span class="string">list,</span> <span class="attr">x:</span> <span class="string">int)</span> <span class="string">-&gt;</span> <span class="attr">int:</span></span><br><span class="line">    <span class="string">""</span><span class="string">"非递归二分查找</span></span><br><span class="line"><span class="string">    返回指定元素在列表中的索引</span></span><br><span class="line"><span class="string">    -1 代表不存在"</span><span class="string">""</span></span><br><span class="line">    <span class="string">mix_index</span> <span class="string">=</span> <span class="number">0</span></span><br><span class="line">    <span class="string">max_index</span> <span class="string">=</span> <span class="string">len(lis)</span> <span class="bullet">-</span> <span class="number">1</span></span><br><span class="line">    <span class="string">while</span> <span class="string">mix_index</span> <span class="string">&lt;=</span> <span class="attr">max_index:</span></span><br><span class="line">        <span class="string">midpoint</span> <span class="string">=</span> <span class="string">(mix_index</span> <span class="string">+</span> <span class="string">max_index)</span> <span class="string">//</span> <span class="number">2</span></span><br><span class="line">        <span class="string">if</span> <span class="string">lis[midpoint]</span> <span class="string">&lt;</span> <span class="attr">x:</span></span><br><span class="line">            <span class="string">mix_index</span> <span class="string">=</span> <span class="string">mix_index</span> <span class="string">+</span> <span class="number">1</span></span><br><span class="line">        <span class="string">elif</span> <span class="string">lis[midpoint]</span> <span class="string">&gt;</span> <span class="attr">x:</span></span><br><span class="line">            <span class="string">max_index</span> <span class="string">=</span> <span class="string">max_index</span> <span class="bullet">-</span> <span class="number">1</span></span><br><span class="line">        <span class="attr">else:</span></span><br><span class="line">            <span class="string">return</span> <span class="string">midpoint</span></span><br><span class="line">    <span class="string">return</span> <span class="number">-1</span></span><br><span class="line"></span><br><span class="line"><span class="string">lists</span> <span class="string">=</span> <span class="string">[1,</span> <span class="number">3</span><span class="string">,</span> <span class="number">5</span><span class="string">,</span> <span class="number">6</span><span class="string">,</span> <span class="number">7</span><span class="string">,</span> <span class="number">8</span><span class="string">,</span> <span class="number">12</span><span class="string">,</span> <span class="number">22</span><span class="string">,</span> <span class="number">23</span><span class="string">,</span> <span class="number">43</span><span class="string">,</span> <span class="number">65</span><span class="string">,</span> <span class="number">76</span><span class="string">,</span> <span class="number">90</span><span class="string">,</span> <span class="number">543</span><span class="string">]</span></span><br><span class="line"><span class="string">res</span> <span class="string">=</span> <span class="string">search(lists,</span> <span class="number">76</span><span class="string">)</span></span><br><span class="line"><span class="string">print(res)</span></span><br></pre>
                      </td>
                    </tr>
                  </table>
                </figure>
                <p>在取列表中间值时使用的语句是 <code>midpoint = (mix_index + max_index) // 2</code>，即地板除，我们可以将其替换为 <code>midpoint = (mix_index + max_index) &gt;&gt; 1</code> 最终得到的结果是相同的。这是因为左移 <code>1</code>位 等效于乘以 <code>2</code>，而右移 <code>1</code> 位等效于除以 <code>2</code>。这样的案例还有很多，此处不再赘述。 至此，我们已经对位运算有了一定的了解，希望你在工作中使用位运算。更多 <code>Saoperation</code> 和知识请扫描下方二维码。 <img src="https://user-gold-cdn.xitu.io/2019/7/12/16be42f3a7eae3fa?w=608&amp;h=304&amp;f=jpeg&amp;s=73490" alt=""></p>
              </div>
              <div class="popular-posts-header">相关文章</div>
              <ul class="popular-posts">
                <li class="popular-posts-item">
                  <div class="popular-posts-title"><a href="/5081.html" rel="bookmark">[Python3网络爬虫开发实战] 1.2-请求库的安装</a></div>
                </li>
                <li class="popular-posts-item">
                  <div class="popular-posts-title"><a href="/5132.html" rel="bookmark">[Python3网络爬虫开发实战] 1.2.1-Requests的安装</a></div>
                </li>
                <li class="popular-posts-item">
                  <div class="popular-posts-title"><a href="/5141.html" rel="bookmark">[Python3网络爬虫开发实战] 1.2.2-Selenium的安装</a></div>
                </li>
                <li class="popular-posts-item">
                  <div class="popular-posts-title"><a href="/5135.html" rel="bookmark">[Python3网络爬虫开发实战] 1.2.3-ChromeDriver的安装</a></div>
                </li>
                <li class="popular-posts-item">
                  <div class="popular-posts-title"><a href="/5153.html" rel="bookmark">[Python3网络爬虫开发实战] 1.2.4-GeckoDriver的安装</a></div>
                </li>
              </ul>
              <div class="reward-container">
                <div></div>
                <button onclick="var qr = document.getElementById('qr'); qr.style.display = (qr.style.display === 'none') ? 'block' : 'none';"> 打赏 </button>
                <div id="qr" style="display: none;">
                  <div style="display: inline-block;">
                    <img src="/images/wechatpay.jpg" alt="崔庆才 微信支付">
                    <p>微信支付</p>
                  </div>
                  <div style="display: inline-block;">
                    <img src="/images/alipay.jpg" alt="崔庆才 支付宝">
                    <p>支付宝</p>
                  </div>
                </div>
              </div>
              <footer class="post-footer">
                <div class="post-tags">
                  <a href="/tags/python/" rel="tag"><i class="fa fa-tag"></i> python</a>
                  <a href="/tags/%E4%BD%8D%E8%BF%90%E7%AE%97/" rel="tag"><i class="fa fa-tag"></i> 位运算</a>
                </div>
                <div class="post-nav">
                  <div class="post-nav-item">
                    <a href="/6829.html" rel="prev" title="Python3 模拟登录并爬取表格数据">
                      <i class="fa fa-chevron-left"></i> Python3 模拟登录并爬取表格数据 </a>
                  </div>
                  <div class="post-nav-item">
                    <a href="/6921.html" rel="next" title="一看就懂，Python 日志 logging 模块详解及应用"> 一看就懂，Python 日志 logging 模块详解及应用 <i class="fa fa-chevron-right"></i>
                    </a>
                  </div>
                </div>
              </footer>
            </article>
          </div>
          <div class="comments" id="gitalk-container"></div>
          <script>
            window.addEventListener('tabs:register', () =>
            {
              let
              {
                activeClass
              } = CONFIG.comments;
              if (CONFIG.comments.storage)
              {
                activeClass = localStorage.getItem('comments_active') || activeClass;
              }
              if (activeClass)
              {
                let activeTab = document.querySelector(`a[href="#comment-${activeClass}"]`);
                if (activeTab)
                {
                  activeTab.click();
                }
              }
            });
            if (CONFIG.comments.storage)
            {
              window.addEventListener('tabs:click', event =>
              {
                if (!event.target.matches('.tabs-comment .tab-content .tab-pane')) return;
                let commentClass = event.target.classList[1];
                localStorage.setItem('comments_active', commentClass);
              });
            }

          </script>
        </div>
        <div class="toggle sidebar-toggle">
          <span class="toggle-line toggle-line-first"></span>
          <span class="toggle-line toggle-line-middle"></span>
          <span class="toggle-line toggle-line-last"></span>
        </div>
        <aside class="sidebar">
          <div class="sidebar-inner">
            <ul class="sidebar-nav motion-element">
              <li class="sidebar-nav-toc"> 文章目录 </li>
              <li class="sidebar-nav-overview"> 站点概览 </li>
            </ul>
            <!--noindex-->
            <div class="post-toc-wrap sidebar-panel">
              <div class="post-toc motion-element">
                <ol class="nav">
                  <li class="nav-item nav-level-2"><a class="nav-link" href="#位运算的基础"><span class="nav-number">1.</span> <span class="nav-text">位运算的基础</span></a>
                    <ol class="nav-child">
                      <li class="nav-item nav-level-3"><a class="nav-link" href="#二进制"><span class="nav-number">1.1.</span> <span class="nav-text">二进制</span></a></li>
                      <li class="nav-item nav-level-3"><a class="nav-link" href="#补码"><span class="nav-number">1.2.</span> <span class="nav-text">补码</span></a></li>
                    </ol>
                  </li>
                  <li class="nav-item nav-level-2"><a class="nav-link" href="#运算符介绍"><span class="nav-number">2.</span> <span class="nav-text">运算符介绍</span></a>
                    <ol class="nav-child">
                      <li class="nav-item nav-level-3"><a class="nav-link" href="#按位与"><span class="nav-number">2.1.</span> <span class="nav-text">按位与</span></a></li>
                      <li class="nav-item nav-level-3"><a class="nav-link" href="#按位或"><span class="nav-number">2.2.</span> <span class="nav-text">按位或</span></a></li>
                      <li class="nav-item nav-level-3"><a class="nav-link" href="#按位异或"><span class="nav-number">2.3.</span> <span class="nav-text">按位异或</span></a></li>
                      <li class="nav-item nav-level-3"><a class="nav-link" href="#按位取反"><span class="nav-number">2.4.</span> <span class="nav-text">按位取反</span></a></li>
                      <li class="nav-item nav-level-3"><a class="nav-link" href="#左移运算"><span class="nav-number">2.5.</span> <span class="nav-text">左移运算</span></a></li>
                      <li class="nav-item nav-level-3"><a class="nav-link" href="#右移运算"><span class="nav-number">2.6.</span> <span class="nav-text">右移运算</span></a></li>
                    </ol>
                  </li>
                  <li class="nav-item nav-level-2"><a class="nav-link" href="#位运算的应用"><span class="nav-number">3.</span> <span class="nav-text">位运算的应用</span></a></li>
                </ol>
              </div>
            </div>
            <!--/noindex-->
            <div class="site-overview-wrap sidebar-panel">
              <div class="site-author motion-element" itemprop="author" itemscope itemtype="http://schema.org/Person">
                <img class="site-author-image" itemprop="image" alt="崔庆才" src="/images/avatar.png">
                <p class="site-author-name" itemprop="name">崔庆才</p>
                <div class="site-description" itemprop="description">崔庆才的个人站点，记录生活的瞬间，分享学习的心得。</div>
              </div>
              <div class="site-state-wrap motion-element">
                <nav class="site-state">
                  <div class="site-state-item site-state-posts">
                    <a href="/archives/">
                      <span class="site-state-item-count">608</span>
                      <span class="site-state-item-name">日志</span>
                    </a>
                  </div>
                  <div class="site-state-item site-state-categories">
                    <a href="/categories/">
                      <span class="site-state-item-count">24</span>
                      <span class="site-state-item-name">分类</span></a>
                  </div>
                  <div class="site-state-item site-state-tags">
                    <a href="/tags/">
                      <span class="site-state-item-count">156</span>
                      <span class="site-state-item-name">标签</span></a>
                  </div>
                </nav>
              </div>
              <div class="links-of-author motion-element">
                <span class="links-of-author-item">
                  <a href="https://github.com/Germey" title="GitHub → https:&#x2F;&#x2F;github.com&#x2F;Germey" rel="noopener" target="_blank"><i class="fab fa-github fa-fw"></i>GitHub</a>
                </span>
                <span class="links-of-author-item">
                  <a href="mailto:cqc@cuiqingcai.com.com" title="邮件 → mailto:cqc@cuiqingcai.com.com" rel="noopener" target="_blank"><i class="fa fa-envelope fa-fw"></i>邮件</a>
                </span>
                <span class="links-of-author-item">
                  <a href="https://weibo.com/cuiqingcai" title="微博 → https:&#x2F;&#x2F;weibo.com&#x2F;cuiqingcai" rel="noopener" target="_blank"><i class="fab fa-weibo fa-fw"></i>微博</a>
                </span>
                <span class="links-of-author-item">
                  <a href="https://www.zhihu.com/people/Germey" title="知乎 → https:&#x2F;&#x2F;www.zhihu.com&#x2F;people&#x2F;Germey" rel="noopener" target="_blank"><i class="fa fa-magic fa-fw"></i>知乎</a>
                </span>
              </div>
            </div>
            <div style=" width: 100%;" class="sidebar-panel sidebar-panel-image sidebar-panel-active">
              <a href="https://tutorial.lengyue.video/?coupon=12ef4b1a-a3db-11ea-bb37-0242ac130002_cqx_850" target="_blank" rel="noopener">
                <img src="https://qiniu.cuiqingcai.com/bco2a.png" style=" width: 100%;">
              </a>
            </div>
            <div style=" width: 100%;" class="sidebar-panel sidebar-panel-image sidebar-panel-active">
              <a href="http://www.ipidea.net/?utm-source=cqc&utm-keyword=?cqc" target="_blank" rel="noopener">
                <img src="https://qiniu.cuiqingcai.com/0ywun.png" style=" width: 100%;">
              </a>
            </div>
            <div class="sidebar-panel sidebar-panel-tags sidebar-panel-active">
              <h4 class="name"> 标签云 </h4>
              <div class="content">
                <a href="/tags/2048/" style="font-size: 10px;">2048</a> <a href="/tags/API/" style="font-size: 10px;">API</a> <a href="/tags/Bootstrap/" style="font-size: 11.25px;">Bootstrap</a> <a href="/tags/CDN/" style="font-size: 10px;">CDN</a> <a href="/tags/CQC/" style="font-size: 10px;">CQC</a> <a href="/tags/CSS/" style="font-size: 10px;">CSS</a> <a href="/tags/CSS-%E5%8F%8D%E7%88%AC%E8%99%AB/" style="font-size: 10px;">CSS 反爬虫</a> <a href="/tags/CV/" style="font-size: 10px;">CV</a> <a href="/tags/Django/" style="font-size: 10px;">Django</a> <a href="/tags/Eclipse/" style="font-size: 11.25px;">Eclipse</a> <a href="/tags/FTP/" style="font-size: 10px;">FTP</a> <a href="/tags/Git/" style="font-size: 10px;">Git</a> <a href="/tags/GitHub/" style="font-size: 13.75px;">GitHub</a> <a href="/tags/HTML5/" style="font-size: 10px;">HTML5</a> <a href="/tags/Hexo/" style="font-size: 10px;">Hexo</a> <a href="/tags/IT/" style="font-size: 10px;">IT</a> <a href="/tags/JSP/" style="font-size: 10px;">JSP</a> <a href="/tags/JavaScript/" style="font-size: 10px;">JavaScript</a> <a href="/tags/K8s/" style="font-size: 10px;">K8s</a> <a href="/tags/LOGO/" style="font-size: 10px;">LOGO</a> <a href="/tags/Linux/" style="font-size: 10px;">Linux</a> <a href="/tags/MIUI/" style="font-size: 10px;">MIUI</a> <a href="/tags/MongoDB/" style="font-size: 10px;">MongoDB</a> <a href="/tags/Mysql/" style="font-size: 10px;">Mysql</a> <a href="/tags/NBA/" style="font-size: 10px;">NBA</a> <a href="/tags/PHP/" style="font-size: 11.25px;">PHP</a> <a href="/tags/PS/" style="font-size: 10px;">PS</a> <a href="/tags/Pathlib/" style="font-size: 10px;">Pathlib</a> <a href="/tags/PhantomJS/" style="font-size: 10px;">PhantomJS</a> <a href="/tags/Python/" style="font-size: 15px;">Python</a> <a href="/tags/Python3/" style="font-size: 12.5px;">Python3</a> <a href="/tags/Pythonic/" style="font-size: 10px;">Pythonic</a> <a href="/tags/QQ/" style="font-size: 10px;">QQ</a> <a href="/tags/Redis/" style="font-size: 10px;">Redis</a> <a href="/tags/SAE/" style="font-size: 10px;">SAE</a> <a href="/tags/SSH/" style="font-size: 10px;">SSH</a> <a href="/tags/SVG/" style="font-size: 10px;">SVG</a> <a href="/tags/Scrapy/" style="font-size: 10px;">Scrapy</a> <a href="/tags/Scrapy-redis/" style="font-size: 10px;">Scrapy-redis</a> <a href="/tags/Scrapy%E5%88%86%E5%B8%83%E5%BC%8F/" style="font-size: 10px;">Scrapy分布式</a> <a href="/tags/Selenium/" style="font-size: 10px;">Selenium</a> <a href="/tags/TKE/" style="font-size: 10px;">TKE</a> <a href="/tags/Ubuntu/" style="font-size: 11.25px;">Ubuntu</a> <a href="/tags/VS-Code/" style="font-size: 10px;">VS Code</a> <a href="/tags/Vs-Code/" style="font-size: 10px;">Vs Code</a> <a href="/tags/Vue/" style="font-size: 11.25px;">Vue</a> <a href="/tags/Webpack/" style="font-size: 10px;">Webpack</a> <a href="/tags/Windows/" style="font-size: 10px;">Windows</a> <a href="/tags/Winpcap/" style="font-size: 10px;">Winpcap</a> <a href="/tags/WordPress/" style="font-size: 13.75px;">WordPress</a> <a href="/tags/Youtube/" style="font-size: 11.25px;">Youtube</a> <a href="/tags/android/" style="font-size: 10px;">android</a> <a href="/tags/ansible/" style="font-size: 10px;">ansible</a> <a href="/tags/cocos2d-x/" style="font-size: 10px;">cocos2d-x</a> <a href="/tags/e6/" style="font-size: 10px;">e6</a> <a href="/tags/fitvids/" style="font-size: 10px;">fitvids</a> <a href="/tags/git/" style="font-size: 11.25px;">git</a> <a href="/tags/json/" style="font-size: 10px;">json</a> <a href="/tags/js%E9%80%86%E5%90%91/" style="font-size: 10px;">js逆向</a> <a href="/tags/kubernetes/" style="font-size: 10px;">kubernetes</a> <a href="/tags/log/" style="font-size: 10px;">log</a> <a href="/tags/logging/" style="font-size: 10px;">logging</a> <a href="/tags/matlab/" style="font-size: 11.25px;">matlab</a> <a href="/tags/python/" style="font-size: 20px;">python</a> <a href="/tags/pytube/" style="font-size: 11.25px;">pytube</a> <a href="/tags/pywin32/" style="font-size: 10px;">pywin32</a> <a href="/tags/style/" style="font-size: 10px;">style</a> <a href="/tags/tomcat/" style="font-size: 10px;">tomcat</a> <a href="/tags/ubuntu/" style="font-size: 10px;">ubuntu</a> <a href="/tags/uwsgi/" style="font-size: 10px;">uwsgi</a> <a href="/tags/vsftpd/" style="font-size: 10px;">vsftpd</a> <a href="/tags/wamp/" style="font-size: 10px;">wamp</a> <a href="/tags/wineQQ/" style="font-size: 10px;">wineQQ</a> <a href="/tags/%E4%B8%83%E7%89%9B/" style="font-size: 11.25px;">七牛</a> <a href="/tags/%E4%B8%8A%E6%B5%B7/" style="font-size: 10px;">上海</a> <a href="/tags/%E4%B8%AA%E4%BA%BA%E7%BD%91%E7%AB%99/" style="font-size: 10px;">个人网站</a> <a href="/tags/%E4%B8%BB%E9%A2%98/" style="font-size: 10px;">主题</a> <a href="/tags/%E4%BA%91%E4%BA%A7%E5%93%81/" style="font-size: 10px;">云产品</a> <a href="/tags/%E4%BA%91%E5%AD%98%E5%82%A8/" style="font-size: 10px;">云存储</a> <a href="/tags/%E4%BA%AC%E4%B8%9C%E4%BA%91/" style="font-size: 10px;">京东云</a> <a href="/tags/%E4%BA%BA%E5%B7%A5%E6%99%BA%E8%83%BD/" style="font-size: 12.5px;">人工智能</a> <a href="/tags/%E4%BB%A3%E7%90%86/" style="font-size: 10px;">代理</a> <a href="/tags/%E4%BB%A3%E7%A0%81/" style="font-size: 10px;">代码</a> <a href="/tags/%E4%BB%A3%E7%A0%81%E5%88%86%E4%BA%AB%E5%9B%BE/" style="font-size: 10px;">代码分享图</a> <a href="/tags/%E4%BC%98%E5%8C%96/" style="font-size: 10px;">优化</a> <a href="/tags/%E4%BD%8D%E8%BF%90%E7%AE%97/" style="font-size: 10px;">位运算</a> <a href="/tags/%E5%85%AC%E4%BC%97%E5%8F%B7/" style="font-size: 10px;">公众号</a> <a href="/tags/%E5%88%86%E4%BA%AB/" style="font-size: 10px;">分享</a> <a href="/tags/%E5%88%86%E5%B8%83%E5%BC%8F/" style="font-size: 10px;">分布式</a> <a href="/tags/%E5%88%9B%E4%B8%9A/" style="font-size: 10px;">创业</a> <a href="/tags/%E5%89%8D%E7%AB%AF/" style="font-size: 12.5px;">前端</a> <a href="/tags/%E5%8D%9A%E5%AE%A2/" style="font-size: 10px;">博客</a> <a href="/tags/%E5%8E%9F%E7%94%9FAPP/" style="font-size: 10px;">原生APP</a> <a href="/tags/%E5%8F%8D%E7%88%AC%E8%99%AB/" style="font-size: 12.5px;">反爬虫</a> <a href="/tags/%E5%91%BD%E4%BB%A4/" style="font-size: 10px;">命令</a> <a href="/tags/%E5%93%8D%E5%BA%94%E5%BC%8F%E5%B8%83%E5%B1%80/" style="font-size: 10px;">响应式布局</a> <a href="/tags/%E5%9E%83%E5%9C%BE%E9%82%AE%E4%BB%B6/" style="font-size: 10px;">垃圾邮件</a> <a href="/tags/%E5%9F%9F%E5%90%8D%E7%BB%91%E5%AE%9A/" style="font-size: 10px;">域名绑定</a> <a href="/tags/%E5%A4%8D%E7%9B%98/" style="font-size: 10px;">复盘</a> <a href="/tags/%E5%A4%A7%E4%BC%97%E7%82%B9%E8%AF%84/" style="font-size: 10px;">大众点评</a> <a href="/tags/%E5%AD%97%E4%BD%93%E5%8F%8D%E7%88%AC%E8%99%AB/" style="font-size: 10px;">字体反爬虫</a> <a href="/tags/%E5%AD%97%E7%AC%A6%E9%97%AE%E9%A2%98/" style="font-size: 10px;">字符问题</a> <a href="/tags/%E5%AD%A6%E4%B9%A0%E6%96%B9%E6%B3%95/" style="font-size: 10px;">学习方法</a> <a href="/tags/%E5%AE%89%E5%8D%93/" style="font-size: 10px;">安卓</a> <a href="/tags/%E5%AE%9E%E7%94%A8/" style="font-size: 10px;">实用</a> <a href="/tags/%E5%B0%81%E9%9D%A2/" style="font-size: 10px;">封面</a> <a href="/tags/%E5%B4%94%E5%BA%86%E6%89%8D/" style="font-size: 18.75px;">崔庆才</a> <a href="/tags/%E5%B7%A5%E5%85%B7/" style="font-size: 12.5px;">工具</a> <a href="/tags/%E5%BC%80%E5%8F%91%E5%B7%A5%E5%85%B7/" style="font-size: 10px;">开发工具</a> <a href="/tags/%E5%BE%AE%E8%BD%AF/" style="font-size: 10px;">微软</a> <a href="/tags/%E6%80%9D%E8%80%83/" style="font-size: 10px;">思考</a> <a href="/tags/%E6%89%8B%E6%9C%BA%E8%AE%BF%E9%97%AE/" style="font-size: 10px;">手机访问</a> <a href="/tags/%E6%95%99%E7%A8%8B/" style="font-size: 10px;">教程</a> <a href="/tags/%E6%95%99%E8%82%B2/" style="font-size: 10px;">教育</a> <a href="/tags/%E6%96%B0%E4%B9%A6/" style="font-size: 12.5px;">新书</a> <a href="/tags/%E6%96%B9%E6%B3%95%E8%AE%BA/" style="font-size: 10px;">方法论</a> <a href="/tags/%E6%97%85%E6%B8%B8/" style="font-size: 10px;">旅游</a> <a href="/tags/%E6%97%A5%E5%BF%97/" style="font-size: 10px;">日志</a> <a href="/tags/%E6%9A%97%E6%97%B6%E9%97%B4/" style="font-size: 10px;">暗时间</a> <a href="/tags/%E6%9D%9C%E5%85%B0%E7%89%B9/" style="font-size: 11.25px;">杜兰特</a> <a href="/tags/%E6%A1%8C%E9%9D%A2/" style="font-size: 10px;">桌面</a> <a href="/tags/%E6%AD%8C%E5%8D%95/" style="font-size: 10px;">歌单</a> <a href="/tags/%E6%B1%9F%E5%8D%97/" style="font-size: 10px;">江南</a> <a href="/tags/%E6%B8%B8%E6%88%8F/" style="font-size: 10px;">游戏</a> <a href="/tags/%E7%84%A6%E8%99%91/" style="font-size: 10px;">焦虑</a> <a href="/tags/%E7%88%AC%E8%99%AB/" style="font-size: 16.25px;">爬虫</a> <a href="/tags/%E7%88%AC%E8%99%AB%E4%B9%A6%E7%B1%8D/" style="font-size: 11.25px;">爬虫书籍</a> <a href="/tags/%E7%8E%AF%E5%A2%83%E5%8F%98%E9%87%8F/" style="font-size: 10px;">环境变量</a> <a href="/tags/%E7%94%9F%E6%B4%BB%E7%AC%94%E8%AE%B0/" style="font-size: 10px;">生活笔记</a> <a href="/tags/%E7%99%BB%E5%BD%95/" style="font-size: 10px;">登录</a> <a href="/tags/%E7%9F%A5%E4%B9%8E/" style="font-size: 10px;">知乎</a> <a href="/tags/%E7%9F%AD%E4%BF%A1/" style="font-size: 10px;">短信</a> <a href="/tags/%E7%9F%AD%E4%BF%A1%E9%AA%8C%E8%AF%81%E7%A0%81/" style="font-size: 10px;">短信验证码</a> <a href="/tags/%E7%AC%94%E8%AE%B0%E8%BD%AF%E4%BB%B6/" style="font-size: 10px;">笔记软件</a> <a href="/tags/%E7%AF%AE%E7%BD%91/" style="font-size: 10px;">篮网</a> <a href="/tags/%E7%BA%B8%E5%BC%A0/" style="font-size: 10px;">纸张</a> <a href="/tags/%E7%BB%84%E4%BB%B6/" style="font-size: 10px;">组件</a> <a href="/tags/%E7%BD%91%E7%AB%99/" style="font-size: 10px;">网站</a> <a href="/tags/%E7%BD%91%E7%BB%9C%E7%88%AC%E8%99%AB/" style="font-size: 11.25px;">网络爬虫</a> <a href="/tags/%E7%BE%8E%E5%AD%A6/" style="font-size: 10px;">美学</a> <a href="/tags/%E8%82%89%E5%A4%B9%E9%A6%8D/" style="font-size: 10px;">肉夹馍</a> <a href="/tags/%E8%85%BE%E8%AE%AF%E4%BA%91/" style="font-size: 10px;">腾讯云</a> <a href="/tags/%E8%87%AA%E5%BE%8B/" style="font-size: 10px;">自律</a> <a href="/tags/%E8%A5%BF%E5%B0%91%E7%88%B7/" style="font-size: 10px;">西少爷</a> <a href="/tags/%E8%A7%86%E9%A2%91/" style="font-size: 10px;">视频</a> <a href="/tags/%E8%B0%B7%E6%AD%8C%E9%AA%8C%E8%AF%81%E7%A0%81/" style="font-size: 10px;">谷歌验证码</a> <a href="/tags/%E8%BF%90%E8%90%A5/" style="font-size: 10px;">运营</a> <a href="/tags/%E8%BF%9C%E7%A8%8B/" style="font-size: 10px;">远程</a> <a href="/tags/%E9%80%86%E5%90%91/" style="font-size: 10px;">逆向</a> <a href="/tags/%E9%85%8D%E7%BD%AE/" style="font-size: 10px;">配置</a> <a href="/tags/%E9%87%8D%E8%A3%85/" style="font-size: 10px;">重装</a> <a href="/tags/%E9%98%BF%E6%9D%9C/" style="font-size: 10px;">阿杜</a> <a href="/tags/%E9%9D%99%E8%A7%85/" style="font-size: 17.5px;">静觅</a> <a href="/tags/%E9%A2%A0%E8%A6%86/" style="font-size: 10px;">颠覆</a> <a href="/tags/%E9%A3%9E%E4%BF%A1/" style="font-size: 10px;">飞信</a> <a href="/tags/%E9%B8%BF%E8%92%99/" style="font-size: 10px;">鸿蒙</a>
              </div>
              <script>
                const tagsColors = ['#00a67c', '#5cb85c', '#d9534f', '#567e95', '#b37333', '#f4843d', '#15a287']
                const tagsElements = document.querySelectorAll('.sidebar-panel-tags .content a')
                tagsElements.forEach((item) =>
                {
                  item.style.backgroundColor = tagsColors[Math.floor(Math.random() * tagsColors.length)]
                })

              </script>
            </div>
            <div class="sidebar-panel sidebar-panel-categories sidebar-panel-active">
              <h4 class="name"> 分类 </h4>
              <div class="content">
                <ul class="category-list">
                  <li class="category-list-item"><a class="category-list-link" href="/categories/C-C/">C/C++</a><span class="category-list-count">23</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/HTML/">HTML</a><span class="category-list-count">14</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/Java/">Java</a><span class="category-list-count">5</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/JavaScript/">JavaScript</a><span class="category-list-count">26</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/Linux/">Linux</a><span class="category-list-count">15</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/Markdown/">Markdown</a><span class="category-list-count">1</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/Net/">Net</a><span class="category-list-count">4</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/Other/">Other</a><span class="category-list-count">39</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/PHP/">PHP</a><span class="category-list-count">27</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/Paper/">Paper</a><span class="category-list-count">2</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/Python/">Python</a><span class="category-list-count">261</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/TypeScript/">TypeScript</a><span class="category-list-count">2</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/%E4%B8%AA%E4%BA%BA%E5%B1%95%E7%A4%BA/">个人展示</a><span class="category-list-count">1</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/%E4%B8%AA%E4%BA%BA%E6%97%A5%E8%AE%B0/">个人日记</a><span class="category-list-count">9</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/%E4%B8%AA%E4%BA%BA%E8%AE%B0%E5%BD%95/">个人记录</a><span class="category-list-count">4</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/%E4%B8%AA%E4%BA%BA%E9%9A%8F%E7%AC%94/">个人随笔</a><span class="category-list-count">15</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/%E5%AE%89%E8%A3%85%E9%85%8D%E7%BD%AE/">安装配置</a><span class="category-list-count">59</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/%E6%8A%80%E6%9C%AF%E6%9D%82%E8%B0%88/">技术杂谈</a><span class="category-list-count">88</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/%E6%9C%AA%E5%88%86%E7%B1%BB/">未分类</a><span class="category-list-count">1</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/%E7%94%9F%E6%B4%BB%E7%AC%94%E8%AE%B0/">生活笔记</a><span class="category-list-count">1</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/%E7%A6%8F%E5%88%A9%E4%B8%93%E5%8C%BA/">福利专区</a><span class="category-list-count">6</span></li>
                  <li class="category-list-item"><a class="category-list-link" href="/categories/%E8%81%8C%E4%BD%8D%E6%8E%A8%E8%8D%90/">职位推荐</a><span class="category-list-count">2</span></li>
                </ul>
              </div>
            </div>
            <div class="sidebar-panel sidebar-panel-friends sidebar-panel-active">
              <h4 class="name"> 友情链接 </h4>
              <ul class="friends">
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/j2dub.jpg">
                  </span>
                  <span class="link">
                    <a href="https://www.findhao.net/" target="_blank" rel="noopener">FindHao</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/ou6mm.jpg">
                  </span>
                  <span class="link">
                    <a href="https://diygod.me/" target="_blank" rel="noopener">DIYgod</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/6apxu.jpg">
                  </span>
                  <span class="link">
                    <a href="https://www.51dev.com/" target="_blank" rel="noopener">IT技术社区</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://www.jankl.com/img/titleshu.jpg">
                  </span>
                  <span class="link">
                    <a href="https://www.jankl.com/" target="_blank" rel="noopener">liberalist</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/bqlbs.png">
                  </span>
                  <span class="link">
                    <a href="http://www.urselect.com/" target="_blank" rel="noopener">优社电商</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/8s88c.jpg">
                  </span>
                  <span class="link">
                    <a href="https://www.yuanrenxue.com/" target="_blank" rel="noopener">猿人学</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/2wgg5.jpg">
                  </span>
                  <span class="link">
                    <a href="https://www.yunlifang.cn/" target="_blank" rel="noopener">云立方</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/shwr6.png">
                  </span>
                  <span class="link">
                    <a href="http://lanbing510.info/" target="_blank" rel="noopener">冰蓝</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/blvoh.jpg">
                  </span>
                  <span class="link">
                    <a href="https://lengyue.me/" target="_blank" rel="noopener">冷月</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="http://qianxunclub.com/favicon.png">
                  </span>
                  <span class="link">
                    <a href="http://qianxunclub.com/" target="_blank" rel="noopener">千寻啊千寻</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/0044u.jpg">
                  </span>
                  <span class="link">
                    <a href="http://kodcloud.com/" target="_blank" rel="noopener">可道云</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/ygnpn.jpg">
                  </span>
                  <span class="link">
                    <a href="http://www.kunkundashen.cn/" target="_blank" rel="noopener">坤坤大神</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/22uv1.png">
                  </span>
                  <span class="link">
                    <a href="http://www.cenchong.com/" target="_blank" rel="noopener">岑冲博客</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/ev9kl.png">
                  </span>
                  <span class="link">
                    <a href="http://www.zxiaoji.com/" target="_blank" rel="noopener">张小鸡</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://www.503error.com/favicon.ico">
                  </span>
                  <span class="link">
                    <a href="https://www.503error.com/" target="_blank" rel="noopener">张志明个人博客</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/x714o.jpg">
                  </span>
                  <span class="link">
                    <a href="http://www.hubwiz.com/" target="_blank" rel="noopener">汇智网</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/129d8.png">
                  </span>
                  <span class="link">
                    <a href="https://www.bysocket.com/" target="_blank" rel="noopener">泥瓦匠BYSocket</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://www.xiongge.club/favicon.ico">
                  </span>
                  <span class="link">
                    <a href="https://www.xiongge.club/" target="_blank" rel="noopener">熊哥club</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/3w4fe.png">
                  </span>
                  <span class="link">
                    <a href="https://zerlong.com/" target="_blank" rel="noopener">知语</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/44hxf.png">
                  </span>
                  <span class="link">
                    <a href="http://redstonewill.com/" target="_blank" rel="noopener">红色石头</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/8g1fk.jpg">
                  </span>
                  <span class="link">
                    <a href="http://www.laodong.me/" target="_blank" rel="noopener">老董博客</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/wkaus.jpg">
                  </span>
                  <span class="link">
                    <a href="https://zhaoshuai.me/" target="_blank" rel="noopener">碎念</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/pgo0r.jpg">
                  </span>
                  <span class="link">
                    <a href="https://www.chenwenguan.com/" target="_blank" rel="noopener">陈文管的博客</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/kk82a.jpg">
                  </span>
                  <span class="link">
                    <a href="https://www.lxlinux.net/" target="_blank" rel="noopener">良许Linux教程网</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/lj0t2.jpg">
                  </span>
                  <span class="link">
                    <a href="https://tanqingbo.cn/" target="_blank" rel="noopener">IT码农</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/i8cdr.png">
                  </span>
                  <span class="link">
                    <a href="https://junyiseo.com/" target="_blank" rel="noopener">均益个人博客</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/chwv2.png">
                  </span>
                  <span class="link">
                    <a href="https://brucedone.com/" target="_blank" rel="noopener">大鱼的鱼塘</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/2y43o.png">
                  </span>
                  <span class="link">
                    <a href="http://bbs.nightteam.cn/" target="_blank" rel="noopener">夜幕爬虫安全论坛</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/zvc3w.jpg">
                  </span>
                  <span class="link">
                    <a href="https://www.weishidong.com/" target="_blank" rel="noopener">韦世东的技术专栏</a>
                  </span>
                </li>
                <li class="friend">
                  <span class="logo">
                    <img src="https://qiniu.cuiqingcai.com/ebudy.jpg">
                  </span>
                  <span class="link">
                    <a href="https://chuanjiabing.com/" target="_blank" rel="noopener">穿甲兵技术社区</a>
                  </span>
                </li>
              </ul>
            </div>
          </div>
        </aside>
        <div id="sidebar-dimmer"></div>
      </div>
    </main>
    <footer class="footer">
      <div class="footer-inner">
        <div class="copyright"> &copy; <span itemprop="copyrightYear">2021</span>
          <span class="with-love">
            <i class="fa fa-heart"></i>
          </span>
          <span class="author" itemprop="copyrightHolder">崔庆才丨静觅</span>
          <span class="post-meta-divider">|</span>
          <span class="post-meta-item-icon">
            <i class="fa fa-chart-area"></i>
          </span>
          <span title="站点总字数">2.6m</span>
          <span class="post-meta-divider">|</span>
          <span class="post-meta-item-icon">
            <i class="fa fa-coffee"></i>
          </span>
          <span title="站点阅读时长">39:54</span>
        </div>
        <div class="powered-by">由 <a href="https://hexo.io/" class="theme-link" rel="noopener" target="_blank">Hexo</a> & <a href="https://pisces.theme-next.org/" class="theme-link" rel="noopener" target="_blank">NexT.Pisces</a> 强力驱动 </div>
        <div class="beian"><a href="https://beian.miit.gov.cn/" rel="noopener" target="_blank">京ICP备18015597号-1 </a>
        </div>
        <script>
          (function ()
          {
            function leancloudSelector(url)
            {
              url = encodeURI(url);
              return document.getElementById(url).querySelector('.leancloud-visitors-count');
            }

            function addCount(Counter)
            {
              var visitors = document.querySelector('.leancloud_visitors');
              var url = decodeURI(visitors.id);
              var title = visitors.dataset.flagTitle;
              Counter('get', '/classes/Counter?where=' + encodeURIComponent(JSON.stringify(
              {
                url
              }))).then(response => response.json()).then((
              {
                results
              }) =>
              {
                if (results.length > 0)
                {
                  var counter = results[0];
                  leancloudSelector(url).innerText = counter.time + 1;
                  Counter('put', '/classes/Counter/' + counter.objectId,
                  {
                    time:
                    {
                      '__op': 'Increment',
                      'amount': 1
                    }
                  }).catch(error =>
                  {
                    console.error('Failed to save visitor count', error);
                  });
                }
                else
                {
                  Counter('post', '/classes/Counter',
                  {
                    title,
                    url,
                    time: 1
                  }).then(response => response.json()).then(() =>
                  {
                    leancloudSelector(url).innerText = 1;
                  }).catch(error =>
                  {
                    console.error('Failed to create', error);
                  });
                }
              }).catch(error =>
              {
                console.error('LeanCloud Counter Error', error);
              });
            }

            function showTime(Counter)
            {
              var visitors = document.querySelectorAll('.leancloud_visitors');
              var entries = [...visitors].map(element =>
              {
                return decodeURI(element.id);
              });
              Counter('get', '/classes/Counter?where=' + encodeURIComponent(JSON.stringify(
              {
                url:
                {
                  '$in': entries
                }
              }))).then(response => response.json()).then((
              {
                results
              }) =>
              {
                for (let url of entries)
                {
                  let target = results.find(item => item.url === url);
                  leancloudSelector(url).innerText = target ? target.time : 0;
                }
              }).catch(error =>
              {
                console.error('LeanCloud Counter Error', error);
              });
            }
            let
            {
              app_id,
              app_key,
              server_url
            } = {
              "enable": true,
              "app_id": "6X5dRQ0pnPWJgYy8SXOg0uID-gzGzoHsz",
              "app_key": "ziLDVEy73ne5HtFTiGstzHMS",
              "server_url": "https://6x5drq0p.lc-cn-n1-shared.com",
              "security": false
            };

            function fetchData(api_server)
            {
              var Counter = (method, url, data) =>
              {
                return fetch(`${api_server}/1.1${url}`,
                {
                  method,
                  headers:
                  {
                    'X-LC-Id': app_id,
                    'X-LC-Key': app_key,
                    'Content-Type': 'application/json',
                  },
                  body: JSON.stringify(data)
                });
              };
              if (CONFIG.page.isPost)
              {
                if (CONFIG.hostname !== location.hostname) return;
                addCount(Counter);
              }
              else if (document.querySelectorAll('.post-title-link').length >= 1)
              {
                showTime(Counter);
              }
            }
            let api_server = app_id.slice(-9) !== '-MdYXbMMI' ? server_url : `https://${app_id.slice(0, 8).toLowerCase()}.api.lncldglobal.com`;
            if (api_server)
            {
              fetchData(api_server);
            }
            else
            {
              fetch('https://app-router.leancloud.cn/2/route?appId=' + app_id).then(response => response.json()).then((
              {
                api_server
              }) =>
              {
                fetchData('https://' + api_server);
              });
            }
          })();

        </script>
      </div>
      <div class="footer-stat">
        <span id="cnzz_stat_icon_1279355174"></span>
        <script type="text/javascript">
          document.write(unescape("%3Cspan id='cnzz_stat_icon_1279355174'%3E%3C/span%3E%3Cscript src='https://v1.cnzz.com/z_stat.php%3Fid%3D1279355174%26online%3D1%26show%3Dline' type='text/javascript'%3E%3C/script%3E"));

        </script>
      </div>
    </footer>
  </div>
  <script src="//cdn.jsdelivr.net/npm/animejs@3.2.1/lib/anime.min.js"></script>
  <script src="//cdn.jsdelivr.net/npm/pangu@4/dist/browser/pangu.min.js"></script>
  <script src="/js/utils.js"></script>
  <script src="/.js"></script>
  <script src="/js/schemes/pisces.js"></script>
  <script src="/.js"></script>
  <script src="/js/next-boot.js"></script>
  <script src="/.js"></script>
  <script>
    (function ()
    {
      var canonicalURL, curProtocol;
      //Get the <link> tag
      var x = document.getElementsByTagName("link");
      //Find the last canonical URL
      if (x.length > 0)
      {
        for (i = 0; i < x.length; i++)
        {
          if (x[i].rel.toLowerCase() == 'canonical' && x[i].href)
          {
            canonicalURL = x[i].href;
          }
        }
      }
      //Get protocol
      if (!canonicalURL)
      {
        curProtocol = window.location.protocol.split(':')[0];
      }
      else
      {
        curProtocol = canonicalURL.split(':')[0];
      }
      //Get current URL if the canonical URL does not exist
      if (!canonicalURL) canonicalURL = window.location.href;
      //Assign script content. Replace current URL with the canonical URL
      ! function ()
      {
        var e = /([http|https]:\/\/[a-zA-Z0-9\_\.]+\.baidu\.com)/gi,
          r = canonicalURL,
          t = document.referrer;
        if (!e.test(r))
        {
          var n = (String(curProtocol).toLowerCase() === 'https') ? "https://sp0.baidu.com/9_Q4simg2RQJ8t7jm9iCKT-xh_/s.gif" : "//api.share.baidu.com/s.gif";
          t ? (n += "?r=" + encodeURIComponent(document.referrer), r && (n += "&l=" + r)) : r && (n += "?l=" + r);
          var i = new Image;
          i.src = n
        }
      }(window);
    })();

  </script>
  <script src="/js/local-search.js"></script>
  <script src="/.js"></script>
  <link rel="stylesheet" href="//cdn.jsdelivr.net/npm/gitalk@1/dist/gitalk.min.css">
  <script>
    NexT.utils.loadComments(document.querySelector('#gitalk-container'), () =>
    {
      NexT.utils.getScript('//cdn.jsdelivr.net/npm/gitalk@1/dist/gitalk.min.js', () =>
      {
        var gitalk = new Gitalk(
        {
          clientID: '4c86ce1d7c4fbb3b277c',
          clientSecret: '4927beb0f90e2c07e66c99d9d2529cf3eb8ac8e4',
          repo: 'Blog',
          owner: 'germey',
          admin: ['germey'],
          id: '1f13d592b9b08699863916fd3f0493fa',
          language: 'zh-CN',
          distractionFreeMode: true
        });
        gitalk.render('gitalk-container');
      }, window.Gitalk);
    });

  </script>
</body>

</html>
